How much ethanol must you add
Suppose a fuel mixture is 7% ethanol and 93% gasoline. How much ethanol (in gallons) must you add to one gallon of the fuel so that the new fuel mixture is 10% ethanol?
You want to add x gallons of 100% ethanol to 1 gallon of 7% ethanol, to get
(1 + x) gallons of 10% ethanol.
1x + 0.07(1) = 0.1(1 + x)
x + 0.07 = 0.1 + 0.1x
x - 0.1x = 0.1 - 0.07
0.9x = 0.03
x = 0.03333 gallons
Does that work?
x + 0.07 = 0.1 + 0.1x
0.03333 + 0.07 = 0.1 + 0.1(0.03333)
0.103333 = 0.10333